1.2. Types of Quadrilaterals

A parallelogram has opposite sides that are equal and parallel. It also has opposite angles that are equal, and its diagonals bisect each other.

A parallelogram is a four-sided polygon (quadrilateral) where pairs of opposite sides are equal in length and parallel to each other. For example, if you drew one, you would notice that both pairs of opposite angles are equal, making quadrilaterals more symmetrical. Furthermore, the diagonals (lines connecting opposite corners) meet at their midpoints, meaning they slice each other into equal parts.

Imagine a table. The short and long sides represent opposite and equal sides of a parallelogram. If you were to draw a line from one corner of the table to the opposite corner, you would create the diagonals that meet at the center of the table.

A rectangle has all angles equal to 90°. Its opposite sides are equal and parallel, and the diagonals are equal in length and they bisect each other.

Rectangles are a special type of parallelogram where every angle is a right angle (90 degrees). This means that the corners are perfect corners. Like parallelograms, opposite sides are still equal in length and parallel to each other. Additionally, the diagonals are not only equal in length but also bisect each other, meaning they cut each other in half.

Think of a standard door. It is a rectangle: its sides are straight, and its corners form right angles. If you were to measure both diagonals from corner to corner, they would be the same length.

A square has all sides equal in length and all angles equal to 90°. The diagonals are equal and also bisect each other at right angles.

A square is a quadrilateral that is both a rectangle and a rhombus, meaning it has both equal sides and right angles. All four sides are of the same length, and each angle measures 90 degrees. The diagonals in a square not only split into equal parts but meet at right angles, creating an 'X' in the center.

Picture a chessboard. Each square on the board has equal sides and right angles. If you were to draw a line from one corner of any square to the opposite corner, you'd see the two diagonals intersect at a right angle.

A rhombus has all sides equal but the angles are not necessarily 90°. Opposite angles are equal, and the diagonals bisect each other at right angles.

A rhombus is also a type of parallelogram and has all its sides of equal length. However, unlike a square, the angles in a rhombus aren't necessarily 90 degrees. The opposite angles are equal, just like in a parallelogram. As for the diagonals, they intersect at right angles but are not of the same length.

Consider a diamond ring. The shape formed by the diamond is a rhombus. Each side of the diamond is equal in length, but the angles can vary, creating a unique look rather than right angles.

In a trapezium (also known as a trapezoid), one pair of opposite sides is parallel.

A trapezium is different from the other quadrilaterals because it only requires one pair of opposite sides to be parallel. These sides are often referred to as the 'bases,' while the non-parallel sides are called 'legs.' The angles in a trapezium can vary widely, depending on the lengths of the sides.

Think of a slice of bread cut diagonally: the base represents the top of the slice, which is parallel to the crust on the opposite side. The two sides of the bread are unequal, just like the legs of the trapezium.

A kite has two pairs of adjacent equal sides. One pair of opposite angles is equal, and the diagonals intersect at right angles.

In a kite, two adjacent sides are equal in length, forming a distinct shape. One pair of opposite angles is equal—specifically, the angles formed by the equal sides. The diagonals in a kite cross each other at right angles, giving them their unique crossed shape.

Think of a flying kite, which has a shape that often resembles the geometric figure. The edges of the sections where the string and fabric meet form equal sides, while the cross-section represents the intersecting diagonals.

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